1. x36912 y1234 State whether the table shows a direct variation. Prove it in two ways. x46810 y5 1520 The variables x and y vary directly. Use the values of x and y to find a constant of proportionality. Then write an equation that relates x to y. y = 3 and x = 4

3. CoCo Puffs Marsh- mallows General Mills is coming out with a new cereal called Hot Cocoa. They experimented with some samples to decide their recipe. We will chart to samples. 240 342 What would the equation be?

4. Identifying Direct Variation Origin (0,0) Constant SLOPE Or check if the values form a proportion

5. If four Oreo cookies contain 220 calories. How many calories would be consumed if you eat three? Find the constant variation first. Write and use the equation to solve for three cookies.

8. The variables x and y vary directly. Use the values to find the constant of proportionality and write an equation that relates x and y. 9. y = kx K is for constant

9. xy 00 21 42 63 84 If it goes through (0,0) The slope The change in y The change in x +2 + 1 y = kx k =

10. xy 32 64 96 128 1510 Oh No! There is no 0! Oh No! There is no 0! xy 32 64 96 128 1510 Relax. We’ll make a space for one xy 412 618 824 1030 You try!

11. I wish everyone would go home and leave me alone! Rearranging Equations (Changing the Point-of-View) Solve for y: What is happening on the side with y? _______________________ What is the opposite? ______________________ x + y = 3

12. I wish everyone would go home and leave me alone! 4x + y = 7x

13. Can the equation be written y = kx? Only combine LIKE terms y = -4x y − 2x = x y − 5 = 5x + 2 y − 2 = 3x − 2 y + 3 = x xy = 5

14. Miles driven Gallons Gas used 562 843 1004 1285 1546 Is this a proportional relationship? Prove it in two ways